The valuation of commuter travel time savings for car drivers: evaluating alternative model specifications

The empirical valuation of travel time savings is a derivative of the ratio of parameter estimates in a discrete choice model. The most common formulation (multinomial logit) imposes strong restrictions on the profile of the unobserved influences on choice as represented by the random component of a preference function. As we progress our ability to relax these restrictions we open up opportunities to benchmark the values derived from simple (albeit relatively restrictive) models. In this paper we contrast the values of travel time savings derived from multinomial logit and alternative specifications of mixed (or random parameter) logit models. The empirical setting is urban car commuting in six locations in New Zealand. The evidence suggests that less restrictive choice model specifications tend to produce higher estimates of values of time savings compared to the multinomial logit model; however the degree of under-estimation of multinomial logit remains quite variable, depending on the context.     

Experimental design influences on stated choice outputs: An empirical study in air travel choice

Discrete choice experiments are conducted in the transport field to obtain data for investigating travel behaviour and derived measures such as the value of travel time savings. The multinomial logit (MNL) and other more advanced discrete choice models (e.g., the mixed MNL model) have often been estimated on data from stated choice experiments and applied for planning and policy purposes. Determining efficient underlying experimental designs for these studies has become an increasingly important stream of research, in which the objective is to generate stated choice tasks that maximize the collected information, yielding more reliable parameter estimates. These theoretical advances have not been rigorously tested in practice, such that claims on whether the theoretical efficiency gains translate into practice cannot be made. Using an extensive empirical study of air travel choice behaviour, this paper presents for the first time results of different stated choice experimental design approaches, in which respective estimation results are compared. We show that D-efficient designs keep their promise in lowering standard errors in estimating, thereby requiring smaller sample sizes, ceteris paribus, compared to a more traditional orthogonal design. The parameter estimates found using an orthogonal design or an efficient design turn out to be statistically different in several cases, mainly attributed to more or less dominant alternatives existing in the orthogonal design. Furthermore, we found that small designs with a limited number of choice tasks performs just as good (or even better) than a large design. Finally, we show that theoretically predicted sample sizes using the so-called S-estimates provide a good lower bound. This paper will enable practitioners in better understanding the potential benefits of efficient designs, and enables policy makers to make decisions based on more reliable parameter estimates.     

How,when and why integrated choice and latent variable models are latently useful

Integrated Choice and Latent Variable (ICLV) models are an increasingly popular extension to discrete choice models that attempt explicitly to model the cognitive process underlying the formation of any choice. This study was born from the discovery that an ICLV model can in many cases be reduced to a choice model without latent variables that fits the choice data at least as well as the original ICLV model from which it was obtained. The failure of past studies to recognize this fact raised concerns about other benefits that have been claimed with regards to the framework. With the objective of addressing these concerns, this study undertakes a systematic comparison between the ICLV model and an appropriately specified reduced form choice model. We derive analytical proofs regarding the benefits of the framework and use synthetic datasets to corroborate any conclusions drawn from the analytical proofs. We find that the ICLV model can under certain conditions lead to an improvement in the analyst's ability to predict outcomes to the choice data, allow for the identification of structural relationships between observable and latent variables, correct for bias arising from omitted variables and measurement error, reduce the variance of parameter estimates, and abet practice and policy, all in ways that would not be possible using the reduced form choice model. We synthesize these findings into a general process of evaluation that can be used to assess what gains, if any, might be had from developing an ICLV model in a particular empirical context.     

Generation of synthetic datasets for discrete choice analysis

Despite the widespread use of synthetic data in discrete choice analysis, little is known about how the methodology used to generate synthetic datasets influences the properties of parameter estimates and the validity of results based on these estimates. That is, there are two potential sources of biases when using synthetic discrete choice data: (1) bias due to the method used to generate the dataset; and, (2) bias due to parameter estimation. The primary objective of this study is to examine bias due to the underlying data generation method. This study compares three methods for generating synthetic datasets and uses design of experiments and analysis of variance methods to investigate the ability to recover estimates for “true” logsum parameters for nested logit models. The method that uses nested logit probabilities to generate the chosen alternative results in unbiased parameter estimates. The method that is based on Gumbel error component approximations reveals that while the error components themselves are unbiased, subtle empirical identification problems can arise when these error components are combined with synthetically generated utility functions. The method that is based on normal error component approximations reveals that all logsum coefficients are biased upwards; the bias dramatically increases for those nests that have a low choice frequency and is most pronounced for those nests with high correlations among alternatives. Based on the results of the analysis, several recommendations for the generation of synthetic datasets for discrete choice analyses are provided.     

Strategic sampling for large choice sets in estimation and application

Many discrete choice contexts in transportation deal with large choice sets, including destination, route, and vehicle choices. Model estimation with large numbers of alternatives remains computationally expensive. In the context of the multinomial logit (MNL) model, limiting the number of alternatives in estimation by simple random sampling (SRS) yields consistent parameter estimates, but estimator efficiency suffers. In the context of more general models, such as the mixed MNL, limiting the number of alternatives via SRS yields biased parameter estimates. In this paper, a new, strategic sampling scheme is introduced, which draws alternatives in proportion to updated choice-probability estimates. Since such probabilities are not known a priori, the first iteration uses SRS among all available alternatives. The sampling scheme is implemented here for a variety of simulated MNL and mixed-MNL data sets, with results suggesting that the new sampling scheme provides substantial efficiency benefits. Thanks to reductions in estimation error, parameter estimates are more accurate, on average. Moreover, in the mixed MNL case, where SRS produces biased estimates (due to violation of the independence of irrelevant alternatives property), the new sampling scheme appears to effectively eliminate such biases. Finally, it appears that only a single iteration of the new strategy (following the initialization step using SRS) is needed to deliver the strategy’s maximum efficiency gains.     

The joint estimation of respondent-reported certainty and acceptability with choice

In the stated choice literature, increasing attention has been paid to methods that seek to close the gap between the choices from these experiments and the choices experienced in the real world. Attempts to produce model estimates that are truer to real market behaviours are especially important for transportation, where many important policy decisions rely on such experiments. A recent approach that has emerged makes use of a certainty index whereby respondents report how certain they are about each choice they make. Additional literature also posits that when making decisions, people first identify an acceptable set of alternatives (alternative acceptability) such that a consideration set if formed and it is from this reduced set that the ultimate choice is made. This paper presents two models that jointly estimates choice and choice certainty and choice and alternative acceptability. This joint estimation allows the modeller to overcome potential endogeneity that may exist between these responses. In comparing choices of differing certainty, surprisingly little difference in marginal sensitivities are found. This is not the case in the alternative acceptability models however. An important finding of this research is that what could be interpreted as preference heterogeneity may in fact be more closely linked to scale. The ramifications of these results on future research are discussed.     

Empirical test of a constrained choice discrete model: Mode choice in São Paulo,Brazil

This paper examines the properties and empirically tests a model of discrete choice which incorporates probabilistic choice set generation. Denominated the Parametrized Logit Captivity (PLC) model, it is a generalization of the well-known “dogit” specification. The PLC model is shown to be theoretically and empirically more flexible than the latter. Work mode choice data collected in a 1977 O/D survey in São Paulo, Brazil, is used to obtain parameter estimates, as well as to evaluate consumer reaction to a series of perturbations in travel time, travel cost and income, for both the PLC and Multinomial Logit models. Comparisons between the two specifications are made in terms of statistical fit, reasonableness of predictions and differences in predictions across models.     

A nested logit model of automobile holdings for one vehicle households

This paper presents a model of automobile choice by single vehicle households. This effort is distinguished from previous disaggregate automobile holdings models primarily by the use of the nested logit model rather than the more restrictive multinomial logit model. We present a 2-step estimation technique that provides consistent and asymptotically efficient parameter estimates, yet is tractable for very large choice sets. Using disaggregate data on 237 one-vehicle households we estimate the unknown parameters on an automobile choice model containing 785 individual makes, models and vintages of passenger vehicles.     

Testing the dogit model with aggregate time-series and cross-sectional travel data

This paper compares dogit and logit specifications of market share models, taking into account the possibility that conclusions might depend on transformations of the explanatory variables of these models. Parameter estimates are obtained both for a time-series urban transit mode of payment model and for a cross-sectional intercity mode choice model. It is demonstrated, using current maximum likelihood techniques extended to take multiple-order autocorrelation of the residuals into account, that the dogit specification is at least equal to, and sometimes clearly superior to, the logit specification irrespective of transformations of explanatory variables.     

Misclassification in travel surveys and implications to choice modeling: application to household auto ownership decisions

Travel surveys that elicit responses to questions regarding daily activity and travel choices form the basis for most of the transportation planning and policy analysis. The response variables collected in these surveys are prone to errors leading to mismeasurement or misclassification. Standard modeling methods that ignore these errors while modeling travel choices can lead to biased parameter estimates. In this study, methods available in the econometrics literature were used to quantify and assess the impact of misclassification errors in auto ownership choice data. The results uncovered significant misclassification rates ranging from 1 to 40% for different auto ownership alternatives. Also, the results from latent class models provide evidence for variation in misclassification probabilities across different population segments. Models that ignore misclassification were not only found to have lower statistical fit but also significantly different elasticity effects for choice alternatives with high misclassification probabilities. The methods developed in this study can be extended to analyze misclassification in several response variables (e.g., mode choice, activity purpose, trip/tour frequency, and mileage) that constitute the core of advanced travel demand models including tour and activity-based models.

     

A note on the use of correlation coefficients for assessing goodness-of-fit in spatial interaction models

The use of correlation coefficients to evaluate the accuracy of spatial interaction models is inappropriate unless such models have been fitted using least squares techniques. In other cases the correlation involves an implicit intercept value and a regression coefficient that may significantly modify the interaction model's estimates. Researchers have not acknowledged the role of these two parameters when the correlation is used. A generalized root mean square error is proposed as an alternative indicator of accuracy that may be used with any model.     

Factors affecting temporal changes in mode choice model parameters

In travel demand forecasting models, parameters are often assumed to be stable over time. The stability of these parameters, however, has been questioned. This study investigates the factors affecting temporal changes in mode choice model parameters using a method proposed by the author that jointly utilises repeated cross-sectional data. In this method, the parameters are assumed to follow functional forms and the parameter changes are modelled endogenously. While the author’s previous studies assumed that all parameters are the same function of the same variable, this study assumes that different parameters are different functions of different variables, including time (year) and macro-economic variables. The paper describes a case study of a journey-to-work mode choice analysis for Nagoya, Japan, that examines 288 combinations of the functional forms and variables. The analysis found that the functions of time had serious over-fitting problems and that parameter changes are more closely related to economic factors.     

Sampling of alternatives for route choice modeling

This paper presents a new paradigm for choice set generation in the context of route choice model estimation. We assume that the choice sets contain all paths connecting each origin–destination pair. Although this is behaviorally questionable, we make this assumption in order to avoid bias in the econometric model. These sets are in general impossible to generate explicitly. Therefore, we propose an importance sampling approach to generate subsets of paths suitable for model estimation. Using only a subset of alternatives requires the path utilities to be corrected according to the sampling protocol in order to obtain unbiased parameter estimates. We derive such a sampling correction for the proposed algorithm.Estimating models based on samples of alternatives is straightforward for some types of models, in particular the multinomial logit (MNL) model. In order to apply MNL for route choice, the utilities should also be corrected to account for the correlation using, for instance, a path size (PS) formulation. We argue that the PS attribute should be computed based on the full choice set. Again, this is not feasible in general, and we propose a new version of the PS attribute derived from the sampling protocol, called Expanded PS.Numerical results based on synthetic data show that models including a sampling correction are remarkably better than the ones that do not. Moreover, the Expanded PS shows good results and outperforms models with the original PS formulation.     

Accounting for stochastic variables in discrete choice models

The estimation of discrete choice models requires measuring the attributes describing the alternatives within each individual’s choice set. Even though some attributes are intrinsically stochastic (e.g. travel times) or are subject to non-negligible measurement errors (e.g. waiting times), they are usually assumed fixed and deterministic. Indeed, even an accurate measurement can be biased as it might differ from the original (experienced) value perceived by the individual.Experimental evidence suggests that discrepancies between the values measured by the modeller and experienced by the individuals can lead to incorrect parameter estimates. On the other hand, there is an important trade-off between data quality and collection costs. This paper explores the inclusion of stochastic variables in discrete choice models through an econometric analysis that allows identifying the most suitable specifications. Various model specifications were experimentally tested using synthetic data; comparisons included tests for unbiased parameter estimation and computation of marginal rates of substitution. Model specifications were also tested using a real case databank featuring two travel time measurements, associated with different levels of accuracy.Results show that in most cases an error components model can effectively deal with stochastic variables. A random coefficients model can only effectively deal with stochastic variables when their randomness is directly proportional to the value of the attribute. Another interesting result is the presence of confounding effects that are very difficult, if not impossible, to isolate when more flexible models are used to capture stochastic variations. Due the presence of confounding effects when estimating flexible models, the estimated parameters should be carefully analysed to avoid misinterpretations. Also, as in previous misspecification tests reported in the literature, the Multinomial Logit model proves to be quite robust for estimating marginal rates of substitution, especially when models are estimated with large samples.     

Measuring uncertainty in discrete choice travel demand forecasting models

In transportation projects, uncertainty related to the difference between forecast and actual demand is of major interest for the decision-maker, as it can have a substantial influence on the viability of a project. This paper identifies and quantifies discrete choice model uncertainty, which is present in the model parameters and attributes, and determines its impact on risk taking for decision-making applied to a case study of the High-Speed Rail project in Portugal. The methodology includes bootstrapping for the parameter variation, a postulated triangular distribution for the mode-specific input and a probabilistic graphical model for the socio-economic input variation. In comparison to point estimates, the findings for mode shift results in a wider swing in the system, which constitutes valuable information for decision-makers. The methodology, findings and conclusions presented in this study can be generalized to projects involving similar models.     

A theoretical and empirical model of trip chaining behavior

This paper addresses the theoretical and empirical issues involved in modeling complex travel patterns. Existing models have the shortcoming of not representing the interdependencies among trip links in trip chains with multiple non-home stops. A theoretical model based on utility theory and explicitly accounting for the trade-offs involved in the choice of multiple-stop chains is developed. Using this theoretical model, utility maximizing conditions for a household's choice of a daily travel pattern are derived. The optimum travel pattern is described in terms of the number of chairs (tours) traveled on a given day and in terms of the number of stops (sojourns) made on each of those chains. For a given household, the form of the optimum pattern is a function of the transportation expenditures (time, cost) required to reach potential destinations. Constraints on the conditions of optimality due to the limited and discrete nature of travel pattern alternatives are also considered. Parameters of the general utility function were estimated empirically using actual travel data derived from a home interview survey taken in Washington, D.C. The multinomial logit model is used to relate utility scores for the alternative travel patterns to choice probabilities. The resulting parameter estimates agree with theoretical expectations and with empirical results obtained in other studies. In order to demonstrate the empirical and theoretical implications of the model, forecasts for various transportation policies (e.g., gasoline price increases, transit fare reductions), as made by this model and by other less complex models, are compared. The results of these comparisons indicate the need for expanding the scope of existing travel forecasting models to explicit considerations of trip chaining behavior.     

Intrapersonal variability and model goodness-of-fit

This paper investigates the effect of day-to-day variability in individuals' travel behavior on the goodness-of-fit of travel demand models estimated with conventional cross-sectional data sets. In particular, this paper examines the effect of day-to-day variability on the goodness-of-fit of least squares regression models of person trip generation. The analytic results show that the conventional R-square goodness-of-fit measure for least squares regression models estimated with cross-sectional data is dependent upon two factors. The first factor is the proportion of the between-person variability that is accounted for by the explanatory variables in the model. The second factor is the proportion of the total variability in the dependent variable that is due to between-person variability. One week activity diary data are used to estimate the relative magnitude of the intrapersonal and interpersonal variability components for a variety of measures of trip-making. This analysis shows that intrapersonal variability may comprise a substantial proportion of the total variability, although the relative magnitude of the intrapersonal variability component varies with trip purpose and across population segments. Generally, however, intrapersonal variability is found to have a considerable effect on the apparent goodness-of-fit of person level trip generation models estimated with cross-sectional data. The paper also illustrates that recognizing the effect of intrapersonal variability on model goodness-of-fit may be useful in interpreting and evaluating model estimation and model transferability results.     

Estimation of a constrained multinomial logit model

Identifying the set of available alternatives in a choice process after considering an individual’s bounds or thresholds is a complex process that, in practice, is commonly simplified by assuming exogenous rules in the choice set formation. The Constrained Multinomial Logit (CMNL) model incorporates thresholds in several attributes as a key endogenous process to define the alternatives choice/rejection mechanism. The model allows for the inclusion of multiple constraints and has a closed form. In this paper, we study the estimation of the CMNL model using the maximum likelihood function, develop a methodology to estimate the model overcoming identification problems by an endogenous partition of the sample, and test the model estimation with both synthetic and real data. The CMNL model appears to be suitable for general applications as it presents a significantly better fit than the MNL model under constrained behaviour and replicates the MNL estimates in the unconstrained case. Using mode choice real data, we found significant differences in the values of times and elasticities between compensatory MNL and semi-compensatory CMNL models, which increase as the thresholds on attributes become active.